Patent application title: Gas turbine rotor assembly methods

Abstract:

Method of assembling a rotor assembly of a gas turbine engine having a
plurality of components. The method comprises in one aspect calculating
the bending forces due to the mass distribution along the rotor. In
another aspect, an optimization routine iterates different rotor
arrangements, comparing the calculated bending moments to determine a set
of component positions that minimizes the bending forces.

Claims:

1-24. (canceled)

25. A method of assembling a rotor assembly of a gas turbine engine having
a plurality of components mounted generally between axially spaced-apart
bearings, the method comprising:for each rotor component, determining a
mass and a location of a center of mass of each component with respect to
an axis of rotation defined by said spaced-apart bearings;using the mass
and the location of the center of mass of each component to calculate
reaction forces at the bearings;calculating the bending moments across
the rotor representative of the forces reacted by the bearings when the
rotor assembly rotatesoptimizing an arrangement of rotor components to
thereby minimize the bending moments of the rotor assembly; andassembling
the rotor using said optimized arrangement of rotor components.

26. The method defined in claim 25, wherein the step of optimizing
comprises determining for each rotor component at least one of an optimum
assembly stacking position and an optimum mass correction to be applied
to said rotor component.

27. The method defined in claim 25, wherein the step of optimizing
comprises determining for each rotor component an optimum assembly
stacking position and an optimum mass correction.

28. The method defined in claim 25, wherein the step of assembling the
rotor further comprises the step of mounting correction masses to a
plurality of rotor components prior to assembly, the correction masses
mounted substantially at the centre of mass of the plurality of rotor
components.

29. The method defined in claim 25, wherein the step of optimizing
includes iteratively calculating a plurality of solutions, and selecting
a solution which minimizes said bending moments.

30. The method defined in claim 25, further comprising: using the mass and
the location of the center of each component to calculate a static
unbalance force associated with each component, and wherein the step of
optimizing also includes minimizing the static unbalance forces.

31. The method defined in claim 30, wherein the step of optimizing
comprises determining for each of the rotor components an optimum
assembly stacking position and an optimum mass correction.

32. The method defined in claim 25, wherein the step of optimizing further
comprises minimizing a total static unbalance force on each bearing.

33. The method defined in claim 32, wherein the step of optimizing
comprises determining for each rotor component an optimum assembly
stacking position and an optimum mass correction.

34. The method as defined in claim 25, wherein the bending moments have
moment arms equal to the axial positions of the centers of mass of the
components relative to each bearing.

35. The method as defined in claim 25, wherein the step of calculating the
bending moments comprises calculating the bending moments across the
rotor representative of the forces induced by correction masses applied
to the rotor assembly to reduce the bearing reaction forces.

36. A method of assembling a rotor assembly of a gas turbine engine, the
rotor assembly including a plurality of rotor components mounted between
axially spaced-apart bearings, the method comprising the steps of:for an
initial assembly of the rotor components, determining initial geometric
data indicative of a radial deviation of a centre of mass of each rotor
component relative to an axis of rotation of the assembly;determining an
initial mass of each rotor component;using the initial geometric data and
mass data to calculate unbalance forces at the rotor supports;calculating
the bending moment distribution acting on the rotor induced by the rotor
components;determining a set of rotor component stacking positions and
associated bearing reactions which minimize bending moments in the rotor;
andassembling the rotor assembly using said set of rotor component
stacking positions.

37. The method defined in claim 36, wherein the step of determining a set
of rotor component stacking positions includes the step of iteratively
calculating said bending moments for a range of possible component
stacking positions, and selecting said set of rotor component stacking
positions from said range.

38. The method defined in claim 36, wherein the step of determining a set
of rotor component stacking positions includes determining mass
corrections to be applied to a plurality of rotor components.

39. The method defined in claim 37, wherein the step of iteratively
calculating includes calculating said bending moments for a range of
possible component stacking positions and possible rotor component mass
corrections, and wherein the step of selecting said set of rotor
component stacking positions includes selecting a set of rotor component
mass corrections.

40. The method defined in claim 36, wherein the step of assembling the
rotor further comprises the step of adding correction masses to a
plurality of rotor components prior to rotor assembly.

41. The method defined in claim 36, wherein the step of calculating the
bending forces of the rotor assembly includes the step of calculating the
sum of the internal moments of the rotor components.

42. The method defined in claim 36, wherein minimizing the bending moments
includes determining moments having moment arms equal to the axial
positions of the components relative to each point.

43. The method defined in claim 36, further comprising: using the mass and
the location of the center of each rotor component to calculate a static
unbalance force associated with each component, and wherein the step of
optimizing also includes minimizing the static unbalance forces.

44. The method defined in claim 36, wherein the step of minimizing the
bending moments comprises determining for each rotor component an optimum
assembly stacking position and an optimum mass correction.

45. The method defined in claim 44, wherein the step of minimizing the
bending moments further comprises minimizing a total static unbalance
force on each bearing.

46. A method of assembling a rotor assembly of a gas turbine engine having
a plurality of components, the method comprising the steps of:determining
bearing reaction loads and a bending moment induced by each component by
using a mass and a center of mass location of each component;determining
an assembly bending moment distribution for a plurality of combinations
of component stacking positions and mass corrections,determining a rotor
arrangement which provides a lowest total bending moment for the
assembly,defining the component stacking positions and mass corrections
associated with the lowest assembly bending moment as optimal stacking
arrangement; andassembling the rotor assembly using said optimal stacking
arrangement.

48. The method as defined in claim 46, further comprising calculating the
static force unbalances of the rotor assembly acting on bearings provided
at opposed ends of the rotor assembly, and wherein defining optimal
stacking arrangement includes defining the component stacking positions
and mass corrections associated with the lowest assembly bending moments
and the lowest static unbalance forces.

49. A method of assembling a rotor assembly of a gas turbine engine having
a set of rotor components, the method comprising the steps of:for each
rotor component, determining a mass and a location of a center of mass
with respect to an axis of rotation of the rotor assembly;using the mass
and the location of the center of mass to determine a static unbalance
force associated with each rotor component;summing the static unbalance
forces of the rotor components to provide a total static unbalance force
of the rotor assembly;providing an optimized rotor arrangement by
optimizing at least one mass correction to be applied to the rotor
components to thereby minimize the total static unbalance force of the
rotor assembly; andassembling the rotor in the optimized rotor
arrangement, including applying said at least one optimized mass
correction to the set of rotor components.

50. The method defined in claim 49, wherein the step of assembling the
rotor further comprises the step of mounting at least one correction mass
to at least one of the rotor components prior to assembly.

51. The method defined in claim 49, wherein the rotor assembly is mounted
for rotation generally between a pair of axially spaced-apart bearings
defining the axis of rotation of the rotor assembly, and wherein the
method further comprising optimizing the at least one correction mass to
thereby minimize the total static unbalance force at each bearing point.

52. The method defined in claim 51, further comprising the step of
determining a residual static unbalance force at the bearing associated
with said optimized rotor arrangement, and providing correction masses to
the rotor assembly to counter said residual static unbalance force.

53. The method defined in claim 49 further comprising correcting for
errors in at least one of detail balance of the components and discrete
stacking angle limitations.

54. A method of assembling a rotor assembly supported by at least two
bearings, the rotor assembly including a plurality of rotor components
each having a center of mass spaced-apart at fixed points along an axis
of rotation of the rotor assembly, the method comprising the steps of:for
an initial assembly of the components, acquiring geometric data
indicative of a radial deviation of a center of mass from a datum for
each component;acquiring mass data for each component;using the radial
deviation and mass data to determine at least one of a total static
unbalance force of the rotor assembly and a total static unbalance force
at each bearing;determining at least one optimized mass correction to be
applied to at least one of the rotor components providing at least one of
a minimum total static unbalance force of the rotor assembly and a
minimum total static unbalance force at each bearing;assembling the
rotor, including applying said at least one optimized mass correction to
the rotor.

55. The method defined in claim 54, wherein the step of determining at
least one optimized mass correction includes the step of iteratively
calculating said forces for a range of possible rotor component mass
corrections, and selecting a set of rotor component mass corrections
which provides at least one of a minimum total static unbalance force of
the rotor assembly and a minimum total static unbalance force at each
bearing.

56. The method defined in claim 54 further comprising correcting for
errors in at least one of detail balance of the components and discrete
stacking angle limitations.

57. A method of assembling a rotor assembly of a gas turbine engine having
a plurality of components, each component having a mass, a center of mass
and a plurality possible stacking positions relative to the other
components, the method comprising the steps of:(a) determining a static
unbalance force vector for each component by using the mass and a
location of the center of mass relative to a datum;(b) determining a
combination of component mass corrections providing a minimum total
static unbalance force for the rotor assembly, including iteratively
calculating said forces for a range of possible component mass correction
combinations and selecting one of said possible combinations providing
said minimum total static unbalance force for the rotor assembly; and(c)
assembling the rotor assembly using said combination of stacking
positions.

58. The method defined in claim 57, further comprising calculating
residual static unbalance forces at a plurality of bearings supporting
the rotor, and applying to the rotor mass corrections associated with the
calculated residual static unbalance forces.

60. A method of assembling a rotor assembly of a gas turbine engine having
a plurality of rotor components mounted for rotation about an axis of
rotation, each rotor component having a mass, a center of mass and
multiple possible angular stacking positions with respect to the other
rotor components, the method comprising the steps of:for a plurality of
said possible stacking positions, determining a position of the center of
mass of each of the components relative to an axis of rotation;for a
plurality of said possible stacking positions, using the mass of each of
the rotor components and respective positions of the centers of mass
thereof to determine an associated static unbalance force of each rotor
component;selecting a set of said rotor mass corrections which provide a
minimal total static unbalance force for the rotor assembly;
andassembling the rotor assembly using said selected set of rotor mass
corrections.

Description:

TECHNICAL FIELD

[0001]The invention relates generally to methods for assembling rotor
components and in particular, high speed rotors such as those in gas
turbine engines.

BACKGROUND OF THE ART

[0002]It is routine for gas turbine engines to have to pass stringent
vibration acceptance tests following production. Rotor eccentricities are
a main source of engine vibration, and eccentricities can be alleviated
by rotor balancing. Balancing is the act of aligning the masses and
rotational centers of the rotor assembly. Complicating matters greatly is
the fact that gas turbine engine rotors typically comprise a plurality of
rotors, such as multiple compressor or turbine stages, which are bolted
or clamped together. The prior art approaches to rotor balancing have had
reasonable success with simple rotors, but not as much with complicated
rotors of the type found in gas turbine engines. So, while methods and
apparatuses already exist for assisting in gas turbine rotor balancing,
errors present in these approaches can tend to be magnified by the
complicated rotor designs, and thus present a risk that an engine will
not meet test requirements despite having been balanced according to
prior art techniques. If an engine does not pass the vibration acceptance
limit, it typically must be disassembled, re-balanced, and reassembled,
which wastes time and resources. Accordingly, there is a need to provide
improvements to rotor assembly.

SUMMARY

[0003]In one aspect, there is provided a method of assembling a rotor
assembly of a gas turbine engine having a plurality of components mounted
generally between axially spaced-apart bearings, the method comprising:
for each rotor component, determining a mass and a location of a center
of mass of each component with respect to an axis of rotation defined by
said spaced-apart bearings; using the mass and the location of the center
of mass of each component to calculate reaction forces at the bearings;
calculating the bending moments across the rotor representative of the
forces reacted by the bearings when the rotor assembly rotates;
optimizing an arrangement of rotor components to thereby minimize the
bending moments of the rotor assembly; and assembling the rotor using
said optimized arrangement of rotor components.

[0004]In accordance with a further general aspect, there is provided a
method of assembling a rotor assembly of a gas turbine engine, the rotor
assembly including a plurality of rotor components mounted between
axially spaced-apart bearings, the method comprising the steps of: for an
initial assembly of the rotor components, determining initial geometric
data indicative of a radial deviation of a centre of mass of each rotor
component relative to an axis of rotation of the assembly; determining an
initial mass of each rotor component; using the initial geometric data
and mass data to calculate unbalance forces at the rotor supports;
calculating the bending moment distribution acting on the rotor induced
by the rotor components; determining a set of rotor component stacking
positions and associated bearing reactions which minimize bending moments
in the rotor; and assembling the rotor assembly using said set of rotor
component stacking positions.

[0005]In accordance with a further general aspect, there is provided a
method of assembling a rotor assembly of a gas turbine engine having a
plurality of components, the method comprising the steps of: determining
bearing reaction loads and a bending moment induced by each component by
using a mass and a center of mass location of each component; and
determining an assembly bending moment distribution for a plurality of
combinations of component stacking positions and mass corrections,
determining a rotor arrangement which provides a lowest total bending
moment for the assembly, defining the component stacking positions and
mass corrections associated with the lowest assembly bending moment as
optimal stacking arrangement; and assembling the rotor assembly using
said optimal stacking arrangement.

[0006]In accordance with a further general aspect, there is provided a
method of assembling a rotor assembly of a gas turbine engine having a
set of rotor components, the method comprising the steps of: for each
rotor component, determining a mass and a location of a center of mass
with respect to an axis of rotation of the rotor assembly; using the mass
and the location of the center of mass to determine a static unbalance
force associated with each rotor component; summing the static unbalance
forces of the rotor components to provide a total static unbalance force
of the rotor assembly; providing an optimized rotor arrangement by
optimizing at least one mass correction to be applied to the rotor
components to thereby minimize the total static unbalance force of the
rotor assembly; and assembling the rotor in the optimized rotor
arrangement, including applying said at least one optimized mass
correction to the set of rotor components.

[0007]In accordance with a further general aspect, there is provided a
method of assembling a rotor assembly supported by at least two bearings,
the rotor assembly including a plurality of rotor components each having
a center of mass spaced-apart at fixed points along an axis of rotation
of the rotor assembly, the method comprising the steps of: for an initial
assembly of the components, acquiring geometric data indicative of a
radial deviation of a center of mass from a datum for each component;
acquiring mass data for each component; using the radial deviation and
mass data to determine at least one of a total static unbalance force of
the rotor assembly and a total static unbalance force at each bearing;
determining at least one optimized mass correction to be applied to at
least one of the rotor components providing at least one of a minimum
total static unbalance force of the rotor assembly and a minimum total
static unbalance force at each bearing; assembling the rotor, including
applying said at least one optimized mass correction to the rotor.

[0008]In accordance with a further general aspect, there is provided a
method of assembling a rotor assembly of a gas turbine engine having a
plurality of components, each component having a mass, a center of mass
and a plurality possible stacking positions relative to the other
components, the method comprising the steps of: determining a static
unbalance force vector for each component by using the mass and a
location of the center of mass relative to a datum; determining a
combination of component mass corrections providing a minimum total
static unbalance force for the rotor assembly, including iteratively
calculating said forces for a range of possible component mass correction
combinations and selecting one of said possible combinations providing
said minimum total static unbalance force for the rotor assembly; and
assembling the rotor assembly using said combination of stacking
positions.

[0009]In accordance with a further general aspect, there is provided a
method of assembling a rotor assembly of a gas turbine engine having a
plurality of rotor components mounted for rotation about an axis of
rotation, each rotor component having a mass, a center of mass and
multiple possible angular stacking positions with respect to the other
rotor components, the method comprising the steps of: for a plurality of
said possible stacking positions, determining a position of the center of
mass of each of the components relative to an axis of rotation; for a
plurality of said possible stacking positions, using the mass of each of
the rotor components and respective positions of the centers of mass
thereof to determine an associated static unbalance force of each rotor
component; selecting a set of said rotor mass corrections which provide a
minimal total static unbalance force for the rotor assembly; and
assembling the rotor assembly using said selected set of rotor mass
corrections.

[0010]Further details of these and other aspects will be apparent from the
detailed description and figures included below.

DESCRIPTION OF THE DRAWINGS

[0011]Reference is now made to the accompanying figures in which:

[0012]FIG. 1 is a schematic of a gas turbine engine including multiple
rotor assemblies;

[0013]FIG. 2 is a flow chart showing a method of balancing a rotor
assembly of the gas turbine engine of FIG. 1 in accordance with a
particular embodiment of the present invention;

[0014]FIG. 3 is a schematic showing a plot of the geometric deviation
vectors when the components or a rotor assembly are arranged in initial
component stacking positions relative to a first datum axis;

[0015]FIG. 4 is a schematic similar to FIG. 3, showing the same center of
mass data but this time relative to a second datum defined relative to
both bearings supports, to thereby provide a datum representative of the
rotor centerline as defined by the two bearing supports;

[0016]FIG. 5 is an isometric view of a high pressure compressor rotor
assembly of the engine of FIG. 1, showing arrows representative of
example static unbalance forces in an XYZ coordinate system;

[0017]FIG. 6 is a view taken along A-A of FIG. 5, showing X and Y force
components of FIG. 5 resolved from the static unbalance forces;

[0018]FIG. 7 is a side view of the rotor assembly of FIG. 5 showing Z
positions of the component centers of mass;

[0019]FIG. 8 is a schematic view of an example rotor assembly showing
component relative stacking positions which result in zero bearing forces
and non-zero bending moments;

[0020]FIG. 9 is a schematic view of the rotor assembly of FIG. 8, this
time showing the component relative stacking positions which result in
zero bearing forces and zero bending moments;

[0021]FIG. 10 is a schematic view of a rotor assembly illustrating loading
which results from rotor unbalances present in the rotor of FIG. 8;

[0023]FIG. 12 is a loading diagram similar to FIG. 10, representing the
rotor assembly loading condition shown in FIG. 9;

[0024]FIG. 13 is a moment diagram similar to FIG. 11, representing the
rotor assembly loading condition shown in FIG. 9;

[0025]FIG. 14 is a schematic view of another example rotor assembly with a
correction mass at the center; and

[0026]FIG. 15 is a schematic view of the rotor assembly of FIG. 14 with a
pair of correction masses at opposed ends of the rotor.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0027]FIG. 1 illustrates a gas turbine engine 10 generally comprising, in
serial flow communication, a fan 12 through which ambient air is
propelled, a multistage compressor 14 for pressurizing the air, a
combustor 16 in which the compressed air is mixed with fuel and ignited
for generating an annular stream of hot combustion gases, and a turbine
section 18 for extracting energy from the combustion gases.

[0028]Generally, the gas turbine engine 10 comprises a plurality of rotor
assemblies having multiple components. For instance, in the illustrated
example, the compressor 14 includes a multi-stage high pressure
compressor (HPC) 22 including five stages of annular rotor components 64,
66, 68, 70 and 72. Each of the five rotor components illustrated in FIG.
1 is provided with forward and aft mounting faces (unindicated). The
components are mounted face-to-face. The forward rotor component 72 has a
cylindrical forward end which defines a journal for mounting a forward
bearing 74. The aft rotor component 64 has a cylindrical aft end which
defines a journal for mounting in an aft bearing 62. The bearings 62 and
74 support the HPC rotor assembly 22 in the engine 10. The bearings 62
and 74 define the engine centerline 76 (i.e. the axis of rotation of the
rotor assembly of the HPC rotor assembly 22).

[0029]Ideally, a high pressure compressor rotor assembly, such as assembly
22 shown in FIG. 1, should be coaxially mounted with the engine
centerline 76 with minimal radial eccentricity to reduce rotor imbalance
during engine operation. Although each rotor component of a gas turbine
engine is manufactured under very tight tolerance constraints, it remains
that even the best made components are slightly off-center or
out-of-balance in some respect. The effect of such slight eccentricities
becomes considerable for larger components, thereby capable of causing
significant radial rotor deflection and, therefore, vibration. For
instance, a concentricity deviation of the mating surfaces between the
two mounting ends of a rotor component may lead to an assembly unbalance
if not taken into account when providing a rotor assembly including the
component. Furthermore, if the axial faces at the two mounting positions
of a rotor component are not perfectly parallel to one another, a planar
deviation exists which is also capable of causing a rotor assembly
unbalance. Centers of masses may also be off-set from the axis of
rotation, also leading to unbalance. Thus, the factors to consider are
many.

[0030]It is well known that high pressure rotor assembly unbalance can be
minimized by adjusting the relative circumferential positions, or
stacking angle, of each component in relation to the other rotor
components so as to cumulatively minimize the de-balancing effect of the
concentricity deviations and the lack of squareness of the mounting ends
of the rotor components. The stacking angle of each component is adjusted
by rotating the component relative to an adjoining component about a
datum or nominal centerline axis in the rotor stack. Therefore, the key
to rotor balancing is to correctly determine what stacking angles are
required to minimize unbalance.

[0031]FIG. 2 is a flow chart representing new methods, described further
below, that can be used to balance the HPC rotor assembly 22 or any other
rotor assembly of a gas turbine engine. The method of FIG. 2 comprises
steps 30 through 50 further described below. FIGS. 3 through 14
illustrate various steps of the methods of FIG. 2 applied to the HPC
rotor assembly 22.

[0032]Now referring to FIG. 2, the step 30 involves measuring the
individual rotor components 64-72 for radial (concentricity) and planar
(parallelism) deviation at the forward and aft mounting ends thereof, for
example, using the approach described above, or any other suitable method
of doing so.

[0033]As indicated in step 32 of FIG. 2, this geometric data is then used
(e.g. by being provided as input to a suitable software routine, such as
those already commercially-available and suitable or adaptable for such
tasks) to determine initial predictions for component stacking positions
based on these geometric parameters, as follows.

[0034]As shown in FIG. 3, the aft bearing 62 is selected to define a first
datum 78 axis for use in stacking, the first datum being defined as a
line normal to the bearing face 62a and passing through the bearing
journal or center b2. The initial predictions for assembly stacking
angles, calculated in step 32, have been calculated using the measured
radial and planar deviation data to minimize assembly eccentricity
relative to first datum 78. (However, it will also be understood that the
first datum axis 78 could instead be determined relative to the forward
bearing 74). Specifically, referring again to FIG. 3, the geometric
deviations of the components are represented by arrows S1-S6. The planar
& radial deviations at the forward mating face of the first component 64
are measured with respect to the bearing position 62. The second
component 66 is positioned/stacked relative to the first component 64 so
as to off-set (as much as possible) the planar and radial deviations of
the first component 64 (represented by arrow S2 in FIG. 3). The third
component 68 is positioned/stacked to off-set (as much as possible) the
summation of planar & radial deviations of the first and second
components 64, 66 combined (represented in FIG. 3 by arrows S3 and S1+S2,
respectively). The initial prediction for stacking position of each
subsequent component of the assembly and the forward bearing 74 is also
determined in a similar fashion. A person skilled in the art will
appreciate that any other suitable method of determining initial
predictions for stacking positions based on the geometric data of the
components of an assembly may be employed. The skilled reader will also
understand that the above stacking exercise will preferably occur
analytically, rather than by physically building a rotor.

[0035]Referring still to FIG. 3, center of mass data for each component is
also desired. Any suitable method may be used to determine the center of
mass of each component. In a preferred approach, a finite element
analysis used to calculate the actual axial position (i.e. the Z
dimension in FIG. 4) of the center of mass for each component, while a
linear interpolation of the radial deviations of the two end point
mounting positions of each component is used to calculate the radial
deviations of the centers of mass. Other suitable techniques may be
employed instead/as well. The radial deviations of the centers of mass of
components 64-72 and the forward bearing 74 relative to first datum 78
are also calculated. FIG. 3 shows the radial deviations of the centers of
mass of components 64-72 and of bearings 62 and 74 expressed graphically
as interconnected points CM1 through CM7, respectively. More
specifically, what is shown is the location (i.e. radial deviation) of
each of the centers of mass CM1 through CM7 with respect to the first
datum 78. Because it was used to define the first datum 78, the center of
mass CM1 of the aft bearing 62 necessarily coincides with the first
datum. The skilled reader will appreciate that the foregoing is a
baseline representation of the rotor which may be obtained using
conventional assembly balancing techniques and software, based upon
acquired geometric deviation data. This baseline is then used in the
present method, as will now be described.

[0036]Defining the first datum in this manner, however, is somewhat
arbitrary. Therefore, according to the present method, it is desirable to
continue the analyses to re-define the center of mass locations for all
rotor components relative to a second datum which better reflects the
actual centerline of rotation of the rotor assembly. Referring
concurrently to FIGS. 2 and 4, the step 34 involves redefining the datum
axis from first datum 78 to second datum 78', which may be done by
conceptually translating relative radial deviation data for the center of
mass of the forward bearing 74 to "zero" deviation. The second datum 78'
represents the rotational axis of the bearings 62 and 74, and thus
provides a second datum which may be used to balance the rotor. Thus, one
translates (e.g. through the use of a suitable computer subroutine) the
center of mass radial deviation data point CM7 to "align" with the second
datum 78' defined together with center of mass radial deviation data
point CM1, and adjusts the points CM2 through CM6 accordingly so that
they are correctly expressed relative to the new datum, as shown
graphically in FIG. 4.

[0037]Any suitable manner of re-expressing the data with reference to the
second datum may be used. An illustrative example of a suitable
translation step can be described conceptually as "pivoting" the
interconnected centers of mass CM1-CM7 about point b2 of FIG. 3 "towards"
the 1st datum 78 (thus conceptually aligning datums 78 & 78') while
maintaining the relative position of the centers of mass CM1-CM7. The
interconnected centers of mass CM1-CM7 are "pivoted" until CM7 reaches
the datum line 78, thereby aligning the aft and forward bearings 62, 74
of the rotor assembly 60 with the datum line (representative now of axis
of rotation of the assembly). The translation takes into account the
axial positions of the centers of mass CM1-CM7 relative to the bearing
locations b1 and b2. Axial distances from point b2 to the centers of mass
CM2 to CM7 are identified by Z1, Z2, Z3, Z4, Z5 and Ztotal in FIG. 4.
Thus, the translation of CM2-CM6 is proportional to the translation of
CM7 to the datum line.

[0038]For example, the translation of CM6 from its "old position relative
to the first datum 78 to its "new" position relative to second datum 78',
can be calculated by the following equation:

RD 6 = R 7 - R 6 ( Z 5 Ztotal )
##EQU00001##

where Rd6 is the new radial distance of CM6 to the second datum 78' once
CM7 has been translated to zero, R6 and R7 are the initial predictions
for radial deviations of the centers of mass CM6 and CM7 relative to the
first datum 78, as shown in FIG. 3, and Z5 and Ztotal are the axial
distances of CM6 and CM7 respectively relative to point b2 (i.e. bearing
62).

[0039]The translation of centers of mass CM2 to CM5 relative to the
centerline 76 (i.e. second datum 78') is similarly calculated using the
above equation but substituting the appropriate data respective to each
center of mass. Notably, the R7 and Ztotal variables in the above
equation remain constant as the intermediate components 64-72 of the
rotor assembly 60 are considered with respect to the translation of the
forward bearing 74 to the datum axis.

[0040]Now referring concurrently to FIGS. 2 and 5, in one aspect the
method comprises determining a static unbalance mass factor, or static
unbalance force of the assembly. This is done in the example presented in
FIG. 2 by determining the static unbalance force for each component (step
36) and then adding the unbalances (steps 38 and 40) to acquire a total
static unbalance for the rotor assembly). Steps 36-40 will now be
discussed in more detail.

[0041]As mentioned, the static unbalance force associated with each
component is determined (step 36 in the flow chart of FIG. 2). Thus, the
static unbalance force of each of the five rotor components 64-72 between
bearing 62 and 74 is determined. The radial deviation at the center of
mass for each component and the component's mass are used to calculate a
static unbalance force for each of the five rotor components 64-72. More
specifically, this may be achieved when the "translated" radial
deviations of the centers of mass CM2-CM6 of the respective components
64-72 relative to the second datum axis 78' are multiplied by the
respective component masses to obtain five static unbalance force vectors
F1-F5, as illustrated in FIGS. 5 and 6, associated respectively with the
five rotor components 64-72. An XYZ coordinate system is defined in FIG.
5 to orient the component static unbalance forces F1-F5 in space. The Z
axis extends axially, nominally along the rotor shaft axis, and the X and
Y axes extend orthogonally radially therefrom. The direction of the
static unbalance forces F1-F5 is determined by the location (i.e. radial
deviation) of the centers of mass CM2-CM6 such that the force vectors
passes therethrough from the datum axis 78', and extending radially
outwards (see FIG. 6). (It will be understood that the vectors F1-F5
remain within a given X-Y plane). The magnitude of each unbalance vector
corresponds to the product of the mass/weight of the rotor component and
the radial deviation of its center of mass. It should be noted that
throughout this application references to unbalance forces are, in the
present examples, actually unbalance levels (i.e. typically expressed in
units of oz-in), and thus not forces, per se. However, the skilled reader
will appreciate that, once an unbalance level is determined, the
resulting unbalance force is derived from the product for the unbalance
and the square of the rotational speed. Consequently, it will be
understood that minimizing static unbalance levels will inherently also
minimizes static unbalance forces (and hence the terms unbalance and
unbalance forces tend to be used interchangeably).

[0042]Next, as shown in step 38 of FIG. 2, in order to sum the individual
unbalances, the X and Y magnitudes and signs (i.e. directions) of the
static unbalance forces F1-F5 are resolved (step 38 in FIG. 2), so that
the components of the vectors can then be summed. (Any suitable approach
for summing the individual force unbalance vectors may be used.) For
example, since F1-F5 are X-Y planar, the X and Y components for each
static unbalance force vectors F1-F5 may be calculated and summed as
follows:

[0043]Static Unbalance Force in the X Direction

Fx=Fx1+Fx2+Fx3+Fx4+Fx5

[0044]Static Unbalance Force in the Y Direction

Fy=Fy1+Fy2+Fy3+Fy4+Fy5

[0045]In step 40 of FIG. 2, the total static unbalance force of the rotor
assembly is then calculated as follows:

F(total)=sqrt(ΣFx2+ΣFy2) Equation (1)

[0046]Referring still to FIG. 2, balancing a rotor assembly may optionally
involve the step 46 of optimizing the total static unbalance force of the
rotor assembly. Any suitable optimization approach may be used. In the
example described herein, optimization is achieved by iteratively
considering various possible component stacking positions/angles, and
determining an optimized stacking position for the components which
results in the lowest rotor assembly static unbalance force (e.g. forcing
F(total) of Equation (1) to zero).

[0047]The total static unbalance force acting on each of the forward and
aft bearings 74 and 62 can also optionally be calculated, indicated as
step 42 of FIG. 2. Any suitable manner of doing so may be used. In the
example presented below, the calculation is based on the Z (axial)
positions of the centers of mass of the intermediate components 64-72
relative to the Z (axial) positions of the forward and aft bearings 74
and 62, as shown in FIG. 7. The X and Y components for each static
unbalance force acting on forward and aft bearings 74 and 62 are
calculated and summed as follows:

[0052]Next, the total static unbalance force acting on each of the forward
and aft bearings 74 (b1) and 62 (b2) is calculated as follows:

[0053]Total Static Unbalance Force on Forward Bearings 74 (b1)

Fb1(total)=sqrt(ΣFxb12+ΣFyb12)

[0054]Total Static Unbalance Force on Aft Bearing 62 (b2)

Fb2(total)=sqrt(ΣFxb22+ΣFyb22)

[0055]The static unbalance forces on each bearing are thus ascertainable,
as a function of axial positioning, mass and radial deviation of center
of mass of the individual components. A balanced rotor may be thought of
as one for which static unbalance forces on each bearing are minimized.
As indicated in step 46 of FIG. 2, optionally the static unbalance forces
on each bearing may be used (i.e. either with or without other
techniques) to determine optimal rotor stacking angles. As mentioned,
optimization may be achieved in any suitable fashion. A preferred
approach is to use a suitable optimization computer program, such
suitable as commercially-available optimization software, to iterate the
possible combinations of component stacking angles (i.e. iterate on
possible component stacking angles such that the resulting static
unbalance force and/or the bending force unbalance are as close to zero
as possible. The output of such an optimization is preferably at least a
set of component stacking angles required to achieve the optimized
solution. The set of component stacking angles and/or one or more
correction weights may then be provided as the rotor assembly
instructions to the assembler, as will now be discussed.

[0056]In another aspect of step 44 of FIG. 2, the present method of
balancing the rotor assembly optionally includes determining and
optimizing (step 46) the internal bending moments or reaction forces
within the rotor. It has been found that a rotor assembly that is
balanced at low speed (i.e. has zero static forces at the bearings) may
still have large internal moments or bending forces which can create
rotor deflections and the associated unbalance during high speed engine
operation. For example, FIG. 8 shows an example four-component rotor
where the total static unbalance force of a rotor assembly is zero, but
the mid span bending forces reacted within the rotor remain significant,
which can lead to rotor deflection and vibration. In contrast, FIG. 9
shows the same rotor stacked differently, and in this stacking the total
static unbalance force of a rotor assembly is also non-zero, but the
unbalance bending forces at mid span are zero, reducing rotor deflection
or bending that would otherwise lead to the creation of additional
unbalance forces. Considering the simplified example of FIG. 8 in more
detail, an unbalance load M*e (i.e. the product of mass M and radial
deviation e) is exerted by each rotor component along a shaft of length
L, and therefore the total static unbalance force is:

F(total)=2Me-2Me=0

and the sum of the moments about each bearing is also zero, so the rotor
is statically and dynamically balanced:

ΣM(Fb1)=ML/8-3ML/8-5ML/8+7ML/8+Fb2L=0, or Fb2=0

ΣM(Fb2)=ML/8-3ML/8-5ML/8+7ML/8+Fb1L=0, or Fb1=0

where Fb1 and Fb2 are the bearing support forces, and the sum of the
moments are the moments about center (L/2) as reacted by the fixed ends
(i.e. the bearings). As the skilled reader will appreciate, the maximum
moment MeL/4 occurs in the center portion of the rotor.

[0057]In comparison, considering the simplified example of FIG. 9, while
the total static unbalance force (F(total)) is the same as for FIG. 8
(i.e. zero), the bearing forces are not zero. By summing the moments
about each bearing the support forces (Fb1, Fb2) can be determined. In a
dynamically balanced rotor the bearing moments are zero, therefore:

ΣM(Fb1)=MeL/8-3eML/8+5MeL/8-7MeL/8+Fb2L=0, or Fb2=Me/2

ΣM(Fb2)=-MeL/8+3eML/8-5MeL/8+7MeL/8+Fb1L=0, or Fb1=-Me/2

where Fb1 and Fb2 are the bearing support forces, and the sum of the
moments are the moments about center (L/2) as reacted by the fixed ends
(i.e. the bearings). The skilled reader will appreciate that it can be
shown that the maximum moment is MeL/16, or 1/4 of the magnitude
represented by the rotor of FIG. 8.

[0058]Alternatively, as discussed further below, a bearing force
calculation of this nature can also be used as a balance correction
calculation. Adding the bearing force or unbalance calculated above to
the rotor as a correction mass (i.e. placed on the rotor at a
specified/known correction plane, as in known in the art) can result in
both rotors being statically and dynamically balanced. Therefore
optimization may be done on correction masses, rather than or in addition
to stacking angles, as will be discussed further below.

[0059]Rotor moments may be determined (44) and optimized (46) in any
suitable manner. In one example shown in FIG. 10, the rotor may be
considered to be a beam simply supported at each by the bearings and
having external point-loadings corresponding to the static unbalance
force of each component (a four-component rotor in a stacking arrangement
similar to FIG. 8 is considered in FIG. 10). Component displacements
multiplied by their mass (as well as any correction masses multiplied by
their radius) provide the beam forces at various locations along the
rotor length. The solution for the moment distribution may then follow
suitable known approaches for determining beam shear, moment loads and
deflections along the beam (i.e. along axis of the rotor). The bearing
forces may then be calculated by summing and equating the moments to zero
about each support (i.e. bearing) or correction plane, as the case may
be. The bearing/correction forces (i.e. Fb1, Fb2) can be determined as
the required reaction loads, as would usually be the case when applying
typical mechanics methods to beam analysis. The moments can then be
summed along the beam. Alternatively, correction forces can be calculated
at any suitable number of stations along the rotor, in the same or other
suitable way.

[0060]Shown in FIG. 11 is a representation of the rotor of FIGS. 8 and 10,
wherein the solid line 90 represents bending moment level as a function
of shaft position, the centreline 92 is the nominal centreline between
the bearings b1, b2, and the dotted line 94 shows a resulting shape
(exaggerated for illustration purposes) of the shaft reacting the
internal bending moments due to unbalance forces. It can be seen from
FIG. 11 that the maximum bending moment (occurring at the center of the
beam in this case) is:

M(max)=MeL/4

while the bending moment area of FIG. 11 (i.e. the area under the curve 90
relative to the nominal centreline 92) is:

M(area)=MeL2/8

[0061]In contrast, shown in FIGS. 12 and 13 are a loading diagrams and a
bending moment diagram, respectively, similar to those of FIGS. 10 and
11, corresponding to the rotor of FIG. 9. As shown in FIG. 12, the
correction forces calculated above (i.e. ±Me/2) have been notionally
added to the rotor of FIG. 9, as balance correction masses applied at the
bearing supports, for purposes of calculating rotor bending moments. The
maximum bending moment is distributed along the shaft and occurs in four
places:

M(max)=MeL/16

, however for this rotor balancing, the moment area is:

M(area)=0

That is, the internal bending moments are more balanced for the rotor of
FIG. 9 as compared to the rotor of FIG. 8.

[0062]It will be understood that the maximum moment in the rotor is not
necessarily related directly to a maximum shaft or rotor deflection.
Rotor deflection is related to the sum of each moment area times the
moment centroidal distance to a given location on the shaft. Preferably,
therefore, the objects of the moment calculations are to a) minimize the
absolute deflection level at key areas like mid span of the bearing
supports and/or b) minimize deflections that are similar to the natural
frequency deflection or mode shapes of the rotor system. The initial
(i.e. simpler) criterion for optimization is preferably minimizing
deflection in critical area(s), such as rotor mid span and/or an aft
support area of the rotor, and as experience with the dynamic
characteristics of a particular rotor design is acquired, other criteria,
such as minimizing deflections similar to the natural frequency
deflection, may be used to further enhance rotor balancing.

[0063]As mentioned, suitable software is commercially available to
calculate moments as a function of axial position for a beam with
identified loads, as well as to calculate resulting rotor internal
bending forces, and to calculate the deflection shape or elastic curve of
the rotor. Any or all of these properties may be used in optimizing rotor
stacking angles, as will now be further discussed.

[0064]Referring again to FIG. 2 step 44, the bending moments of the rotor
assembly 22 may be considered in balancing the rotor. While bending
moment may be considered in any suitable manner, in the example present
herein, the internal bending moments resulting from the unbalance of each
of the components 62-72 are individually calculated and optimized for the
rotor assembly. The bending moments resulting from the force unbalance
associated with each rotor component are calculated for various stacking
angles, with a goal of minimizing the maximum bending moment (M(max)) as
well as minimizing the bending moment area (M(area)), as discussed above.

[0065]Preferably, the bending moment optimization is done at the same time
as the static unbalance force optimization. However, the method of
balancing a rotor assembly using bending moments analysis may optionally
be carried out considering only the bending moments--i.e. without also
considering the static unbalance force. In such an analysis, the
correction or bearing forces (Fb1, Fb2) are calculated for use in the
bending force unbalance for the assembly, and then optimized by way of
iteration as described above. The optimal assembly bending moment
unbalance is determined (i.e. M(max) and M(area) are minimized) and the
corresponding stacking positions are output as the optimal stacking
positions, or used in determining and placing correction masses.

[0066]The skilled reader will appreciate that optimizations result in
compromise. For example, when considering rotor unbalance and rotor
moments, a reduction of one may not result in a reduction of the other.
Depending on the circumstances, one approach may be better than the
other. For example, for a flexible rotor, which deflects easily in the
presence of internal moments (whereas a rigid rotor does not), it has
been found that a moment-based optimization will tend to yield better
results than an unbalance optimization--hence if only one is to be done,
although any of the above may be employed, a moment optimization tends to
be preferred. If multiple correction planes are available, a two variable
optimization (i.e. moment and unbalance) are preferably both used.

[0067]As shown as step 48 in FIG. 2, the components 64-72 of the rotor
assembly 60 are then physically stacked in the optimal stacking positions
to thereby provide a rotor with minimal static unbalance force, minimal
bearing forces and/or minimal bending moments, as the case may be,
according to the above teachings. More specifically, the components 62-74
are assembled, preferably one by one, in sequentially order, preferably
from the last compressor stage forwards. Depending on the mechanical
connections provided, the rotor components may be assembled using the
assembly angles rounded to the nearest bolt holes of such connections.

[0068]As mentioned, stacking the rotor preferably begins at one end, with
the first component 64 being positioned in a suitable fixture. The second
component 66 is positioned adjacent the mating face of the first
component 64 and rotated until the angular position thereof relative to
the first component 64 is optimal, according to the a set of instructions
output by the above process. The remaining components 68 to 72 are
stacked in a similar manner.

[0069]One will appreciate that an optimized rotor assembly will typically
continue to include some deviation and unbalance. The deviation and
unbalance data calculated as described above, however, may be used to
guide the selection and placement of correction masses to the rotor. As
indicated in step 50 of FIG. 2, To achieve such a result, residual
unbalance forces at the bearings are calculated and correction masses are
added to (or mass suitably removed from) the assembled rotor.

[0070]Optionally, correction masses may be taken into consideration during
the above described optimization process of step 46. For example, rather
than optimizing on assembly (stacking angles) as described above,
optimization may rather (or additionally) focus on corrections to mass to
provide the desired balance. The method of balancing embodied herein
allows the correction forces to be examined at the same time as (or in
preference to) the static and/or bending forces. Correction unbalances
are determined by the product of the correction mass(es) and radial (X-Y)
placement(s) applied at a given axial (Z) position along the rotor
length. Therefore, calculating the correction masses may in fact be done
ahead of the rotor build stage, which further assists in achieving a zero
force balance by allowing correction masses to be installed during rotor
build, perhaps at planes along the rotor which are inaccessible once the
rotor is fully assembled. It will be understood that if the unbalance
generated by a component mass displacement is corrected by mass
removal/addition at the component's center of mass, or close by, both the
unbalance forces and bending moments will be simultaneously minimized in
the rotor assembly.

[0071]FIGS. 14 and 15 are illustrative examples showing the influence of
the location of correction masses. In the presence of a force unbalance
Fu at the axial center of the rotor assembly R, the addition of a
correction mass C, providing an opposing force Fc such that Fc=Fu, placed
in the axial center (in this example) of the rotor R balances the rotor
assembly R both statically and dynamically (i.e. both unbalance forces
and bending moments are countered). It can be seen that the rotor
deflection shape for the rotor assembly R, denoted by line 80, remains
aligned with the axis of rotation, and hence a well-balanced rotor
assembly results. However, in comparing FIG. 14 with FIG. 15, it can be
seen that if a pair of correction masses C, each providing an opposing
force Fc/2 such that Fc=Fu, is added at axial ends of the same rotor
assembly R, the rotor assembly R is both statically balanced (i.e. static
unbalance forces are balanced, but bending moments are not--i.e. a moment
exists within the rotor at centre span, as is well understood by the
skilled reader). This rotor would result in a bowed rotor deflection
shape, denoted by the line 82, during engine operation, particularly with
flexible rotors turning at high speed, which may result in rotor
vibration.

[0072]Therefore, the method of balancing a rotor assembly preferably takes
into consideration static unbalance force, correction mass forces and
bending force distributions based on component geometric and mass data;
thereby creating a complete geometric balancing process eliminating the
need and cost of conventional physical balancing approaches. Moreover,
the additional focus on bending and correction forces provides an
effective solution in balancing flexible rotors that tend to be very
responsive to the presence of bending moments.

[0073]It will be understood that when correction masses are installed
(actually or virtually, i.e. during analysis) at some earlier stage in
the balancing process, the static forces and bending moments introduced
by the correction masses are preferably factored in, along with the other
components, in order to analytically determine the optimal stacking
positions of the "corrected" rotor assembly. One skilled in the art will
appreciate that the step of adding correction masses may be carried out
in any suitable manner and at any suitable point in the above process,
however not all correction mass approaches will yield identical results.

[0074]In summary, presented are a number of techniques which may be used
individually or in conjunction with one another (and/or other techniques)
to balance a rotor assembly. The above description is meant to be
exemplary only, and one skilled in the art will recognize that changes
may be made to the embodiments described without departing from the scope
of the invention disclosed. For example, the method of balancing
described above can be applied, with suitable modification, to an
overhung rotor assembly (i.e. one in which the bearings are not located
at both ends). Also, any suitable approach to providing initial
predictions for geometric stacking of the rotor may be used, or may be
omitted altogether, with the optimization beginning instead with any
selected rotor assembly stacking arrangement. Still other modifications
which fall within the scope of the present invention will be apparent to
those skilled in the art, in light of a review of this disclosure, and
such modifications are intended to fall within the appended claims.